University of QatarCollege of Engineering

Numerical Methods (GENG 300)Fall 2014

HW#1Due on Thursday October 30, 2014

Problem#1Convert the Binary numbers to base 10 number 2 marks

1) 110011002) 111010103) 100010114) 11000101

Problem#2 4 marksThe derivative of f (x) = 1/(1 − 3x2) is given by

6 x(1−3x 2)2

Do you expect to have difficulties evaluating this function at x = 1.337? Try it using 3 and 4-digit arithmetic with chopping.

Problem#3 4 marks

The Maclaurin series expansion for cos(x) is

cos ( x )=1− x2

2+ x

4

4 !− x

6

6 !+ x

8

8!

Starting with the simplest version, cos x = 1, add terms one at a time to estimate cos(π/4). After each new term is added, compute the true and approximate percent relative errors. Use your pocket calculator to determine the true value. Add terms until the absolute value of the approximate error estimate falls below an error criterion conforming to two significant figures.